cppdraft_translate/cppdraft/sf/cmath/riemann/zeta.md

[sf.cmath.riemann.zeta]

29 Numerics library [numerics]

29.7 Mathematical functions for floating-point types [c.math]

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.19 Riemann zeta function [sf.cmath.riemann.zeta]

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floating-point-type riemann_zeta(floating-point-type x); float riemann_zetaf(float x); long double riemann_zetal(long double x);

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Effects: These functions compute the Riemann zeta function of their respective argumentsx.

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Returns: ζ(x), where ζ is given by Formula 29.39 andx is x.

ζ(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩∞∑k=1k−x,for x>111−21−x∞∑k=1(−1)k−1k−x,for 0≤x≤12xπx−1sin(πx2)Γ(1−x)ζ(1−x),for x<0(29.39)